Question: 2 Repeated Digits

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Hello Brent,

I employed a different method to get the solution. Please let me know if correct.

Step 1 : Total number of 3 digits greater than 499 = 500(5*10*10)
Step 2 : Total number of 3 digits with similar number = 5(555,666,777,888,999)
Step 3 : Total number of 3 digits with exactly one number same = 360(5*9*8)
Step 4 : Total number of 3 digits with exactly two numbers same = 500 - 5 - 360 = 135
greenlight-admin's picture

Perfect approach!

Thank you.

Why is 922 not included?
greenlight-admin's picture

922 is just one of the many possible outcomes I listed in order to get a better idea of what the possible outcomes look like.

Once I listed some outcomes, I saw that there are three CATEGORIES of outcomes that satisfy the given requirements.

Those three categories are:
1) different, same, same
2) same, different, same
3) same, same, different

So, the 45 outcomes in category 1 include numbers like 511, 744, 877, etc. This category ALSO includes 922.
So, 922 IS included among the 45 outcomes in category 1.

Does that help?

Cheers,
Brent

My only problem with this is why there should be 1 at last stage. 5*9*1. Please, kindly explain that to me. Why no 5*9*8. Thanks
greenlight-admin's picture

In stage 3, the last digit must be the SAME as another number.
For example, at 1:50, the 3rd digit must the same as the 2nd digit.

So, if during stage 2, the digit 7 was selected, then the 3rd digit must be 7.
So, there's only ONE way to select the 3rd digit so that it matches the 2nd digit.

Does that help?

Cheers,
Brent

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